Whitetiger, that is not true for this condition. The interlock to keep the tractor from starting works completely off the PTO lever. If the light on the dash is OFF, then the tractor should start normally. Pierre may find that with a rotary cutter or other implement attached, the PTO will slip, but he will have to have the engine completely shut down when he hooks anything to the PTO stub. I agree with you that this is NOT the best/safest way to operate, especially if the PTO won't slip at all when turned OFF. In an emergency, this would work, but not be something I'd want to do all the time.
Dopplegangar, you are correct that this requires splitting the tractor at the rear differential. That is the 1st step in the New Holland Repair Manual. That's easy to say, but a huge job on the TC45D, especially since the OP's photo shows a soft cab. The operator platform has to be raised up/removed to allow the differential split. The repair is fairly simple and straight-forward, but getting to the problem is where the big labor hours/cost will be.
Pierre: I'm very sorry you have this problem. My tractor has a few over 1700 hours and the PTO still works just like the day I brought it home. I've been extremely lucky and am very careful with engaging/disengaging. I think once your PTO clutch/brake is repaired, you'll likely never have another problem with it. I just wish it was not going to be so expensive for you.